Iiijluence nf Masses of Iron on the Mariners'' Coinpass. 347 



see, ill the first instance, why 2 cos ip : sin (p : : 1 : cos I' ; nor, if 

 that is granted, can I make out from it that tan 8' = 2 cot (p. 

 It is clear that the expressions (!) and (2) are to each other as 

 2 cos ;fi to sin cf ; hnt why i" this particular instance have they 

 also the ratio of 1 to cos 8' ? Again, if 

 cos 5'= \ tan. (f) 



cos 2'= «=-: therefore, 



2 cot. ip ' ' 



1 tan V 



2 cot. © •= 77-= - ■ \, ■) not tan. 8', as in the text. 



cos V sin. c' ' ' 



Mr. Bonnycastle can very probahly clear all this up immediately; 

 and if he would be good enough to do so, it would be an obliga- 

 tion to others, who may not see further than myself. N. 



To Mr. T'dloo/t. 



Sir, — I FiiEL myself much obliged to your Correspondent N. 

 for having pointed out a probable source of embarrassment in 

 the paper on Magnetism, which you inserted in your Magazine 

 for June last. The passage occurs in page 453 ; where, speaking 

 of the position a needle would assume if influenced by the mag- 

 netism of a sphere of iron, I have said: 



" Were the needle acted on by no other attraction than that 

 of the sphere, its position would be such that 

 tan 8'= 2 cos <p." 



In this expression, as well as in the proportion from which it 

 is derived, viz. 



'* 2 cos ip : sin <p : : 1 : cos 8'," 

 an error of the press has been committed by substituting cos for 

 cot. 



Making this correction, the truth of the equation 



tan 8'= 2 cot <p 

 follows very readily from the proportion, 



2 cos <p : sin 9 : : 1 : cot 8' ; 

 for thence 



c>/ sin ip , , 



cot 6 = - - = i tan <p, 



1 _ 2 



col y liiii ip ' 



tan 8' = 2 cot f. 

 Rut it has also been observed, that there is a want of clearness 

 in the origin of the proportion 



2. cos f : .-.in (f : : \ : cot 8'. 

 Which difficiilty I am inclined to attribute to the former ; had 

 X X 2 the 



